Linear Exponential Quadratic Gaussian Covariance Steering

• URL: http://arxiv.org/abs/2609.12463v1
• Date: Fri, 11 Sep 2026 05:54:35 GMT
• Title: Linear Exponential Quadratic Gaussian Covariance Steering
• Abstract summary: We show that the LEQG covariance steering controller--still a linear state feedback--can no longer be written in closed form.<n>We prove the existence-uniqueness of solution for the LEQG covariance steering problem in the neighborhood of the known risk-neutral optimal solution.
• Score: 0.13764085113103217
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We formulate and analyze the linear exponential quadratic Gaussian (LEQG) covariance steering problem in continuous time over a given deadline (finite time horizon). The solution for this problem can be seen as a risk-sensitive Schrödinger bridge between Gaussian endpoints in the linear quadratic setting. Unlike the risk-neutral case, the LEQG covariance steering controller--still a linear state feedback--can no longer be written in closed form. We show that the optimal controller is parameterized by a symmetric matrix solving an algebraic equation that encodes the implicit dependence on the risk-sensitivity parameter. We explain how the structure of this optimal controller significantly generalizes the existing results for the risk-neutral case. Building on these results, for the matched noise and input channel case, we prove the existence-uniqueness of solution for the LEQG covariance steering problem in the neighborhood of the known risk-neutral optimal solution. We give an illustrative numerical example.

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